The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 90% of the lead to decay? (Round your answer to two decimal places.)

It will take 10.96 hours for 90% of the lead to decay.

Step-by-step explanation:

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t

This means that the amount can be modeled by the following function:

In which A(0) is the initial amount and r is the decay rate.

Has a half-life of 3.3 hours.

This means that . We use this to find r.

So

How long will it take for 90% of the lead to decay?

This is t for which , that is, 100 - 90 = 10% of the initial amount.

It will take 10.96 hours for 90% of the lead to decay.

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have